The Statistical Steering Theorem

This monograph presents The Statistical Steering Theorem, a mathematical framework establishing strict upper and lower bounds for scalar path distance without relying on continuous curve fitting or complex sensor telemetry. Designed for autonomous navigation, kinematics, and spatial analysis, it addresses the failure of classical calculus integrals when processing high-frequency, noisy trajectory data. By applying strict convexity (Jensen's Inequality on absolute slopes) and concavity (Tangent-Line Bounds) to spatial slope distributions, the theorem proves that actual path distance is tightly bounded by net displacement, systematic drift, and stochastic steering variance.